复杂网络中的离散非线性薛定谔方程
Discrete nonlinear Schrödinger equation in complex networks
摘要：
研究了有限格点上离散非线性薛定谔方程（DNLS）的动力学性质。从最近邻相互作用的周期性链开始，我们随机插入连接晶格中遥远的站点对的链接。使用本地化的初始条件，我们专注于时间平均的初始站点的占用概率作为一个功能的复杂程度的晶格和非线性。我们观察到，自陷发生在越来越大的值的非线性参数的晶格连接性的增加，而接近完全耦合网络的限制，本地化变得更加首选。对于非线性值高于一定的阈值，我们发现一个重入本地化过渡，即本地化时，长距离债券的数量是小的，然后离域和增强运输在中间债券数量，而接近完全连接的限制本地化重新出现。
英文摘要：
We investigate dynamical aspects of the discrete nonlinear Schrödinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites across the lattice. Using localized initial conditions we focus on the time averaged probability of occupation of the initial site as a function of the degree of complexity of the lattice and nonlinearity. We observe that selftrapping occurs at increasingly larger values of the nonlinearity parameter as the lattice connectivity increases, while close to the fully coupled network limit, localization becomes more preferred. For nonlinearity values above a certain threshold we find a reentrant localization transition, viz. localization when the number of long distant bonds is small followed by delocalization and enhanced transport at intermediate bond numbers while close to the fully connected limit localization reappears.
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